Combinatorial Network-Based Manifold Topological Deep Learning for Image Analysis
Abstract
Medical image analysis remains fundamentally challenging because of the intricate geometric and topological structures present in medical data. Conventional convolutional neural networks model images as regular Euclidean grids, limiting their ability to preserve geometric relationships and higher-order structural information. Recently, manifold topological deep learning (MTDL) has emerged as a promising paradigm that integrates deep learning with geometric and topological representations. Nevertheless, existing methods have not yet fully exploited discrete manifold structures within combinatorial complex neural networks. To bridge this gap, we introduce CNMTDL, a MTDL framework that integrates Hodge decomposition with a combinatorial attention mechanism. In our approach, medical images are represented as discrete manifolds and decomposed into three Hodge components. Features extracted from these components are concatenated and embedded into a combinatorial complex architecture, enabling enhanced higher-order message passing between $0$-cells and $2$-cells through attention-based blocks. We evaluate CNMTDL on six two-dimensional and three-dimensional datasets from the MedMNIST v2 benchmark, demonstrating its effectiveness for medical image analysis.
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BibTeX
@misc{wachira2026combinatorial,
title = {{Combinatorial Network-Based Manifold Topological Deep Learning for Image Analysis}},
author = {Alice Wachira and Xiang Liu and Zhe Su and Yiying Tong and Ge Wang and Guo-Wei Wei},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.25453},
eprint = {2609.25453},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.25453},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Combinatorial Network-Based Manifold Topological Deep Learning for Image Analysis
AU - Alice Wachira
AU - Xiang Liu
AU - Zhe Su
AU - Yiying Tong
AU - Ge Wang
AU - Guo-Wei Wei
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.25453
UR - https://arxiv.org/abs/2609.25453
AB - Medical image analysis remains fundamentally challenging because of the intricate geometric and topological structures present in medical data. Conventional convolutional neural networks model images as regular Euclidean grids, limiting their ability to preserve geometric relationships and higher-order structural information. Recently, manifold topological deep learning (MTDL) has emerged as a promising paradigm that integrates deep learning with geometric and topological representations. Nevertheless, existing methods have not yet fully exploited discrete manifold structures within combinatorial complex neural networks. To bridge this gap, we introduce CNMTDL, a MTDL framework that integrates Hodge decomposition with a combinatorial attention mechanism. In our approach, medical images are represented as discrete manifolds and decomposed into three Hodge components. Features extracted from these components are concatenated and embedded into a combinatorial complex architecture, enabling enhanced higher-order message passing between $0$-cells and $2$-cells through attention-based blocks. We evaluate CNMTDL on six two-dimensional and three-dimensional datasets from the MedMNIST v2 benchmark, demonstrating its effectiveness for medical image analysis.
ER -